Problem: The following line passes through point $(-2, 7)$ : $y = -\dfrac{13}{9} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(-2, 7)$ into the equation gives: $7 = -\dfrac{13}{9} \cdot -2 + b$ $7 = \dfrac{26}{9} + b$ $b = 7 - \dfrac{26}{9}$ $b = \dfrac{37}{9}$ Plugging in $\dfrac{37}{9}$ for $b$, we get $y = -\dfrac{13}{9} x + \dfrac{37}{9}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-2, 7)$